Problem: What do the following two equations represent? $5x-2y = -5$ $10x-4y = -2$
Putting the first equation in $y = mx + b$ form gives: $5x-2y = -5$ $-2y = -5x-5$ $y = \dfrac{5}{2}x + \dfrac{5}{2}$ Putting the second equation in $y = mx + b$ form gives: $10x-4y = -2$ $-4y = -10x-2$ $y = \dfrac{5}{2}x + \dfrac{1}{2}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.